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3

Discount rate & NPV formulas

Hey,

1) I am a little confused about the discount rate. Could anyone help me to understand the formula to calculate this discount rate
2) Which formula do you use after to calculate the NPV? (NPV = (Cash flows)/( 1+r)^t)?

Thanks!

Hey,

1) I am a little confused about the discount rate. Could anyone help me to understand the formula to calculate this discount rate
2) Which formula do you use after to calculate the NPV? (NPV = (Cash flows)/( 1+r)^t)?

Thanks!

Hi, typically you are given the discount rate. But you can make an estimation (use average interest rate). 2) to calculate NPV you need to take future value and divide it by (1+discount rate)^number of periods — Anonymous B on Oct 16, 2020

Thanks! What I mean is that I am not sure why in Table 8 we have discount rate of 1; 0.90; 0,82; 0.75... it is decreasing with years... — Anonymous A on Oct 19, 2020 (edited)

3 answers

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Best Answer

In nutshell:

Would you prefer to receive 1000 USD now or in one year? I guess now. So basically the 1000 USD in one year have a "smaller" value than 1000 USD now.

Let's build on that.

If I give you 1000 USD now, you could invest them, say at 5%.

So in one year you would have 1050 USD. This means that having 1000 USD now is the same as having 1050 USD in one year.

In formulas: 1050 USD in one year are equal to

1050 USD/(1+5%)^1 year

or

1050/(1+0,05), which gives 1000 USD as a result. The NPV of 1050 USD in one year is equal to 1000 USD now.

But what happens in two years?

If I give you 1000 USD now, then you could invest them at 5% rate per year. At the end of the first year you would have 1050 USD (see above), and at the end of the second year 1050*(1+0,05), or 1102,05 USD.

This means that 1000 USD now are like 1102,5 in two years. The discount rate of 5% must be applied for two periods, so 1102,5 USD/(1+5%)^2, or 1102,50/(1,05)^2, or 1102,50/1,1025 - equal to 1000 USD.

I hope this helps!

In nutshell:

Would you prefer to receive 1000 USD now or in one year? I guess now. So basically the 1000 USD in one year have a "smaller" value than 1000 USD now.

Let's build on that.

If I give you 1000 USD now, you could invest them, say at 5%.

So in one year you would have 1050 USD. This means that having 1000 USD now is the same as having 1050 USD in one year.

In formulas: 1050 USD in one year are equal to

1050 USD/(1+5%)^1 year

or

1050/(1+0,05), which gives 1000 USD as a result. The NPV of 1050 USD in one year is equal to 1000 USD now.

But what happens in two years?

If I give you 1000 USD now, then you could invest them at 5% rate per year. At the end of the first year you would have 1050 USD (see above), and at the end of the second year 1050*(1+0,05), or 1102,05 USD.

This means that 1000 USD now are like 1102,5 in two years. The discount rate of 5% must be applied for two periods, so 1102,5 USD/(1+5%)^2, or 1102,50/(1,05)^2, or 1102,50/1,1025 - equal to 1000 USD.

I hope this helps!

(edited)

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Nothing much to add to the other posts, just one thing:

Very few cases actually ask you to use this formula to calculate NPVs. And even if they do, there is sometimes a catch in the question that allows you to not actually calculat it.

To give an example: if you're comparing two projects. Project A has a lower nominal payment at a later stage than Project B, there might be the question regarding the NPV, but for the financial decision making it doesn't matter, because Project B will always be profitbale. You can state that and then discuss other, more qualitative considerations.

Nothing much to add to the other posts, just one thing:

Very few cases actually ask you to use this formula to calculate NPVs. And even if they do, there is sometimes a catch in the question that allows you to not actually calculat it.

To give an example: if you're comparing two projects. Project A has a lower nominal payment at a later stage than Project B, there might be the question regarding the NPV, but for the financial decision making it doesn't matter, because Project B will always be profitbale. You can state that and then discuss other, more qualitative considerations.

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Hi there,

Two main points

1) You are almost always given discount rate (but you need to ask). A discount rate is essentially your opportunity cost on the money invested. So, any of the following #s could end up being the discount rate: company hurdle rate, cost of capital, cost of equity, interest rates, historical % returns on other projects, expected returns on other existing projects/investments

2) NPV is almost always done into perpituity in cases (i.e. Cash Flows / (1+r). You rarely need to do the ^t. Furthermore, you may have to subtract the growth rate from r...if your future cash flows are projected to grow

Hi there,

Two main points

1) You are almost always given discount rate (but you need to ask). A discount rate is essentially your opportunity cost on the money invested. So, any of the following #s could end up being the discount rate: company hurdle rate, cost of capital, cost of equity, interest rates, historical % returns on other projects, expected returns on other existing projects/investments

2) NPV is almost always done into perpituity in cases (i.e. Cash Flows / (1+r). You rarely need to do the ^t. Furthermore, you may have to subtract the growth rate from r...if your future cash flows are projected to grow